We can use the point-slope formula to write an equation for this line. The point-slope form of a linear equation is: (y - color(blue)(y_1)) = color(red)(m)(x - color(blue)(x_1))
Where (color(blue)(x_1), color(blue)(y_1)) is a point on the line and color(red)(m) is the slope.
Substituting the values from the point in the problem and the slope from the problem gives:
(y - color(blue)(6)) = color(red)(-2)(x - color(blue)(-4))
(y - color(blue)(6)) = color(red)(-2)(x + color(blue)(4))
We can also solve for y to put the equation in slope-intercept form. The slope-intercept form of a linear equation is: y = color(red)(m)x + color(blue)(b)
Where color(red)(m) is the slope and color(blue)(b) is the y-intercept value.
y - color(blue)(6) = (color(red)(-2) xx x) + (color(red)(-2) xx color(blue)(4))
y - color(blue)(6) = color(red)(-2)x + (-8)
y - color(blue)(6) = color(red)(-2)x - 8
y - color(blue)(6) + color(blue)(6) = color(red)(-2)x - 8 + color(blue)(6)
y - 0 = color(red)(-2)x - color(blue)(2)
y = color(red)(-2)x - color(blue)(2)
